Various structural systems have parts that move when actuated. For example, microelectromechanical systems (MEMS) devices may include resonant structures that oscillate when actuated with a forcing function. For any actuator working on a structural system, the forcing function can be decomposed into orthogonal subcomponents that act on the set of all structural Eigenmodes. The amplitudes of each subcomponent describes how well-suited the actuator is to stimulating the corresponding Eigenmode. For resonant systems, the forcing function is used to cause the structural response to be dominated by vibrations corresponding to one Eigenmode.
Piezoelectric unimorphs are common MEMS actuators. An electric field within the piezoelectric film produces a mechanical stress. Attaching the film to another material creates a stress gradient through the composite structure that induces a curvature. FIG. 1 shows a piezoelectric material 110 deposited on a substrate 120. When a voltage is applied to piezoelectric material 110, the resulting stress gradient induces a curvature in substrate 120.